This project studies several types of instrumentation used either in biomedical or biochemical applications. In the field of NMR we have concluded a calculation of the optimal design of magnetization transfer experiments to measure first-order rate constants when the associate spin-lattice relaxation time, T1, is initially unknown, but when an initial range can be given for this parameter. A single experiment can be designed optimally to measure either the rate constant, T1, or any linear combination of these parameters. A continuing project analizes and compares noise in 2D and 3D PET images. Our current approach relies on the use of phantoms, while in the future this project will be extended to a Monte Carlo simulation study. Other work in progress includes the development of an automatic quantitative image analysis to provide accurate non-subjective interpretation and quantitation of intra-vascular ultra sound (IVUS) images which are used to guide clinical interventions. The immediate task is to provide a reliable method to evaluate quantitatively the volumetric progression of atherosclerosis by detecting closed loop edges on IVUS images. A further project is that of developing and improving a multimodal maximum likelihood reconstruction algorithm. It uses high resolution MRI segmentation data in reconstructing PET images of the brain. Work in progress focuses on techniques for improving the convergence of the reconstruction algorithm. A quantitative comparison has been made of gel and capillary-zone electrophoresis for separating peaks resulting from measurements of peak motion and peak-broadening of small DNA fragments of different sizes. It was found, using realistic parameters in the comparison, that the use of capillary-zone electrophoresis is able to speed up separations by at least an order of magnitude. A further project measures peak shapes in gel electrophoresis. Results obtained so far indicate that peaks are generally asymmetric. A theory based on random walks has been developed to interpret this deviation from Gaussian behavior in terms of the statistical properties of entanglement times in the gels. Thus far, the theory has been shown to be in good qualitative agreement with observed data. Further experiments are presently being performed to test the quantitative agreement between the theory and data taken on proteins and DNA. A monograph by U. Shmueli and G.H. Weiss, An Introduction to Crystallographic Statistics has been published by Oxford University.